Question

Бассейн имеет прямоугольную форму.Одна из его сторон на 6 м больше другой. Он окружен дорожкой ширина которой 0,5 м.Найдите стороны бассейна,если площадь окружающей дорожки 15м2 Помогите решить задачу через x Дам 20баллов)))

Answer 1

Пусть х - меньшая сторона бассейна, тогда х+6 - большая
Площадь бассейна х(х+6)
Меньшая длина бассейна с дорожкой х+0,5+0,5=х+1 
Большая сторона бассейна с дорожкой х+6+0,5+0,5=х+7
Составим уравнение:
(х+1)(х+7)-х(х+6)=15
x^2+8x+7-x^2-6x=15
2x=8
x=4 Меньшая сторона бассейна
х+6=4+6=10 - большая сторона

Answer 2

Problem Analysis

We are given that a rectangular pool has one side that is 6 meters longer than the other side. The pool is surrounded by a track that is 0.5 meters wide. The area of the track is given as 15 square meters. We need to find the dimensions of the pool.

Solution

Let's assume that the shorter side of the pool is x meters. Then the longer side of the pool will be x + 6 meters.

The area of the pool can be calculated by multiplying the length and width of the pool:

Area of the pool = x * (x + 6)

The area of the track surrounding the pool is given as 15 square meters. The total area of the pool and the track is the sum of the areas of the pool and the track:

Total area = Area of the pool + Area of the track

Substituting the values, we have:

Total area = x * (x + 6) + 15

To solve this equation, we can expand and rearrange it:

x^2 + 6x + 15 = x^2 + 6x + 15

Since the x^2 and 6x terms cancel out, we are left with:

15 = 15

This equation is true for any value of x. Therefore, the dimensions of the pool can be any value as long as the equation is satisfied.

In conclusion, the dimensions of the pool cannot be determined uniquely based on the given information.